Method and means for correcting measuring instruments

ABSTRACT

The invention relates to measuring instruments, preferably of the kind measuring absorbances, in an object, of electromagnetic radiation in at least two spectral ranges, such as IR instruments, and DXR, meaning Dual X-ray instruments, and more specifically to the determination of properties of food or feed, such as the fat content in milk or meat. The invention relates in particular to a method of providing a correction for a slave instrument of the kind measuring properties of an object by exposing the object to electromagnetic radiation, in particular X-rays, in at least two spectral ranges and obtaining one or more object responses thereto. The responses obtained being preferably based on detecting attenuation and/or reflection and/or scatter of the electromagnetic radiation in/from the object by use of one or more detectors and are obtained in a form where they express properties of the object either directly or via a transformation.

TECHNICAL FIELD

The present invention relates to measuring instruments, preferably ofthe kind measuring absorbances, in an object, of electromagneticradiation in at least two spectral ranges, such as IR instruments, andDXR, meaning Dual X-ray instruments, and more specifically to thedetermination of properties of food or feed, such as the fat content inmilk or meat.

BACKGROUND ART

Spectral instruments measuring e.g. infrared absorbances at severalwavelengths in order to determine contents of specific components in aliquid such as milk are well known. Also X-ray analysis for determiningthe fat content of meat has been known for several years.

Typically such instruments apply regression analysis and multivariatecalibration. Such analysis is known from e.g. the applicant's own PCTapplication No. WO 95/16201 disclosing the determination of extraneouswater in milk samples using regression analysis and multivariatecalibration. Further, the applicant's PCT application No. WO 98/43070discloses measurement of acetone in milk using IR spectroscopy andmultivariate calibration. The transfer of calibrations from oneinstrument to another has been discussed in US patent No. U.S. Pat. No.5,459,677 disclosing a “Calibration transfer for analytical instruments”and US patent No. U.S. Pat. No. 5,559,728 disclosing “Calibrationtransfer for second order analytical instruments” and in the applicantsUS patent No. U.S. Pat. No. 5,933,792 “Method of standardizing aspectrometer”.

The applicant's WO 93/06460 discloses an infrared attenuation measuringsystem, including data processing based on multivariate calibrationtechniques, and the applicants U.S. Pat. No. 5,252,829 discloses adetermination of urea in milk with improved accuracy using at least partof an infrared spectrum.

As disclosed in WO 01/29557 the properties a medium of food or feed,such as the fat content of meat, may be determined by use of dual X-rayabsorptiometry, the medium being a raw material of food or feed, aproduct or intermediary product of food or feed, or a batch, sample orsection of the same, the method comprising—scanning substantially all ofthe medium by X-ray beams having at least two energy levels, including alow level and a high level,—detecting the X-ray beams having passedthrough the medium for a plurality of areas (pixels) of the medium,—foreach area calculating a value, A_(low), representing the absorbance inthe area of the medium at the low energy level,—for each areacalculating a value, A_(high) representing the absorbance in the area ofthe medium at the high energy level, further comprising for each areagenerating a plurality of values being products of the type A_(low)^(n)*A_(high) ^(m) wherein n and m are positive and/or negative integersor zero, and predicting the properties of the medium in this area byapplying a multivariate calibration model to the plurality of values,wherein the calibration model defines relations between the plurality ofvalues and properties of the medium. The advantage over the prior art isa more accurate determination of the properties, such as the fat contentin the medium. The accuracy is specifically improved over the prior artwhen measuring layers of varying thickness. A further advantage is dueto the fact that using the described method almost the whole product ismeasured instead of a sample thereof. Generally, extraction of a samplefrom—an inhomogeneous medium will introduce an error, because the samplemay not be truly representative.

Preferably the calibration model is obtained by use of a multivariateregression method being included in the group comprising PrincipalComponent Regression (PCR), Multiple Linear Regression (MLR), PartialLeast Squares (PLS) regression, and Artificial Neural Networks (ANN).

A problem related to the prior art:

It is well known, that when a number of measurement instruments measurethe same sample, each instrument will generally produce an instrumentspecific signal if no specific actions are taken to ensure that thesignals produced by the instruments are identical for an identicalsample. It is equally well known that it is desirable to be able tomanufacture measuring instruments, which generate the same signal whenexposed to the same sample.

Calibration of an instrument may remedy the problem. However themultivariate calibration, which is applied for the DXR analysis—asdescribed above and in the published WO 01/29557—is a delicate matterrequiring a number of known reference samples, which typically have tobe analyzed by an officially recognized reference method. The provisionof such analysis results of the delicate perishable calibration samplesconsisting of various mixed samples of meat and fat which have to behandled very carefully preferably as frozen items—are time consuming,tedious and expensive. Further the calculations required for providingthe calibration are time consuming too and therefore, expensive. Thesedrawbacks are emphasized when a large number of instruments must becalibrated. Furthermore, when such calibrations must be performed often,such as regularly due to drifting in the instruments, the calibrationmethod may strongly influence the usefulness of the instruments in anegative manner.

Thus, an object of the present invention is to provide a method, whichseeks to avoid the above-mentioned drawbacks. Accordingly it is anobject to disclose a method and instruments enabling a single highlysophisticated calibration developed on a master instrument to be appliedto all other instruments in a series of similar instruments.

More specifically it is an object to provide a method of adjustment orcorrection for a series of instruments in such a manner that they canuse the same calibration.

The present invention is specifically useful to measurements on meatperformed by use of Dual X-ray equipment designed for measuring fat andareal density in meat, as well as for detecting foreign bodies in a meatsample. Such a measurement should, in order to obtain an acceptableaccuracy, detect X-ray attenuation at at least two X-ray energies.According to the particular aspect of the present invention an X-rayequipment comprising two X-ray sources and two X-ray detectors is usedfor measuring the absorbances. Measurements performed with suchequipment have shown to be extremely delicate as the amount of X-raysabsorbed by adipose (fat) and muscle tissue only differs slightly,thereby demanding extreme care in calibrating the instrument.

Thus, another object of the present invention is to provide a method,which ease set-up of an Dual-X-ray instrument so that it is capable ofproducing accurate measurement of fat and areal density in meat.

A further object is to allow for less restrictive instrumentspecifications, enabling the use of cheaper components having rathercoarse tolerances, thereby reducing the total cost of the instrument.

DISCLOSURE OF THE INVENTION

In a first aspect of the present invention and in accordance with theobjects of the invention, a method of providing a correcting for a slaveinstrument is suggested. The slave instrument is preferably of the kindmeasuring properties of an object by exposing the object toelectromagnetic radiation, in particular X-rays, in at least twospectral ranges and obtaining one or more object responses thereto. Theresponses obtained being preferably based on detecting attenuationand/or reflection and/or scatter of the electromagnetic radiationin/from the object by use of one or more detectors and are obtained in aform where they express properties of the object either directly or viaa transformation. The suggested method of correcting comprises:

-   -   obtaining, for a plurality of stable objects, a set of responses        comprising one or more pair of related responses (Q_(low) ^(s)        and Q_(high) ^(s)) representing measurements in the at least two        spectral ranges performed with the slave instrument and a set of        responses, comprising one or more pair of related responses        (Q_(low) ^(m) and Q_(high) ^(m)) representing measurements in        the at feast two spectral ranges performed with a master        instrument,        -   to each pair of related responses (Q_(low) ^(s) and Q_(high)            ^(s)) of the slave instrument corresponds a pair of related            responses (Q_(low) ^(m) and Q_(high) ^(m)) of the master            instrument,        -   and to each element in each pair of responses (Q_(low) ^(s)            and Q_(high) ^(s)) of the slave instrument corresponds an            element in the corresponding pair of responses (Q_(low) ^(m)            and Q_(high) ^(m)) of the master instrument;    -   determining based on the sets of responses a correcting function        being a functional relationship between a ratio of related        responses of the master instrument and a sum of a plurality of        terms, each term being a product of a correcting coefficient        (B_(i)) and powers of related responses (Q_(low) ^(s) and        Q_(high) ^(s)) of the slave instrument, wherein each response        being raised to a power being a positive or negative real        number, or zero, thereby determining a first set of correcting        coefficients (B₀; B₁; B₂ . . . ) being multiplied on each of the        terms; and    -   storing the first set of correcting coefficients (B₀; B₁; B₂ . .        . ) in memory means included in or adapted for communication        with data processing means included in or adapted for        communication with the slave instrument.

Thanks to the provision of a correcting function, each instrument may bebrought in a condition where each of them produces similar, such asidentical, responses on identical objects. Thus, by utilizing thecorrecting functions the responses produced by slave instruments can betransformed into so-called standardized responses (or correctedresponses) which when subjected to a calibration function depending onsuch standardized responses may provide the desired knowledge about thephysical properties of a measured object.

Thus, while calibrations typically are tedious and expensive due torequired chemical analysis of each object used in calibration and due tothe high number of calibration objects needed for a satisfyingcalibration the correcting function may be obtained by use of a set ofstandardizing objects and a corresponding set of master responsespreferably stored in any suitable medium, preferably a data memory, suchas a disc delivered together with the set of standardizing objects oralternatively, a report written on paper.

Thereby, the most common job to be performed in connection with thepresent invention—is to achieve the same responses from the slaveinstrument, as would have been provided by the master instrumentmeasuring the same object. This advantage is believed to be achieved bythe present invention.

Thus, a calibration model will thereby be transferable between allstandardized instruments, and the measurements, such as the X-raydetermination of fat in meat, will be much easier to handle. The presentmethod for correcting a slave instrument, such as a Dual-X-rayequipment, using a limited number of stable standardizing objects, istherefore considered very useful, and therefore also the method ofobtaining a correcting function used in performing the correction.

Thanks to the saved set of correcting coefficients (B₀; B₁; B₂ . . . )the slave instrument inclusive the data processing means and storedprograms will able to correct successive measurements on unknown objectsproviding substantially correct measurements results based on acalibration elaborated for a master instrument. This will be explainedfurther in the detailed description.

The term response as used in this application means is always related toa detected signal and generally it will be related to at least twodetected signals. Accordingly the response may be considered to be amathematical transformation of a number of signals resulting from adetector. Such signals may typically be digital signals provided by ananalogue to digital converter converting electrical signals, provided bythe detectors, into digital representations of the signals. Thus, aresponse, for instance the intensity (I), is in this connectiontypically generated from a detector signal, typically being a voltage,current or digital representation, by applying a mathematical relationto the detector signal, such as I=f(U) where f is a mathematicalfunction and U is the voltage provided by a detector. In that sense allthe responses considered are typically resulting from transformations ofsignals into responses. However, it is contemplated that the inventionis applicable also in embodiments where the signals from the detectors,for instance a digital representation (e.g. as binary numbers), are usedas responses as these signals, of course, express properties of theobject.

Depending on the mode of employment of the invention, such responses areeither used as they are provided, for instance by mathematicalrelations, or are transformed into transformed responses. Typicalexamples of responses are intensity, which may be considered as aresponse used as it is provided, transmittance through an objectbeing—derived from measuring the intensity with and without the object,and therefore preferably being considered as a derived response,absorbance being derived from the transmittance, reflectance, which alsomay be considered as a response used as it is provided, and aKubelka-Munk transformation being applied to the reflectance.

It should be noted that the designations “high” and “low” are used ingeneral for designating two values where one of these is higherrelatively to the other value. Furthermore, two or more separate sourcesmay be utilized in connection with the present invention as well acombination of one source and two filters emitting a low and a highenergy beam.

The method according to the present invention comprises preferably thestep of initially at a manufactures site measuring the plurality ofstable objects on a master instrument, thereby obtaining the set ofresponses representing measurements performed with the master instrument(Q_(low) ^(m) and Q_(high) ^(m)),

-   -   storing the set of responses (Q_(low) ^(m) and Q_(high) ^(m)) as        a set of constant values in memory means, which is accessible        from a slave instrument, when measuring the corresponding stable        objects on a slave instrument in order to carry out a method of        correcting according to the present invention.

Thereby, the responses needed for providing the correcting function iseasy accessible and the workload connected with the method may bereduced.

Typically and preferably, the set of responses measured by the masterinstrument is stored in memory means included in or adapted forcommunication with data processing means included in or adapted forcommunication with the slave instrument.

The so-called “standardization” or correction is preferably based on aset of stable items which initially have been measured on a masterinstrument and all responses have been recorded on a recording mediumsuch as a disc or ROM, which in the future follows the specific set ofstable objects in view of the fact that such a set of stable objectstypically is expensive a specific set of stable object could be used formany slave instruments, e.g. applied once a year during a maintenancevisit by a service technician or when major changes are made to theinstrument (such as a change of radiation source or a detector). Inpreferred embodiments such standardized responses and/or any specificcalibration may be accessible through computer means of well-known art,e.g. through the Internet on a pay per use principle.

Typically and preferably, the determination of the correcting functionbeing based on a regression method, which has proven to be a veryefficient manner to obtain the correcting function. In preferredembodiments, the regression method is selected from the group consistingof principal component regression, multiple linear regression, partialleast squares regression, and artificial neural networks. The partialleast square method has proven to be especially useful.

It is generally preferred, that the correcting function comprises aplurality of terms of the following form Q_(low) ^(n1)*Q_(high) ^(m1)wherein n1 and m2 are real numbers and/or integers, and n1 is positive.In accordance with preferred and practical very useful embodiments it ispreferred that the correcting function comprises at least three of thefollowing terms: Q_(low), Q_(high), Q_(low) ², Q_(high) ² andQ_(low)/Q_(high). In order to achieve a higher accuracy in thecorrecting, more terms may preferably be added to the correctingfunction such that the correcting function comprises at least three ofthe following terms:

-   -   Q_(low)*Q_(high); Q_(low) ²*Q_(high); Q_(low)*Q_(high) ²;        Q_(low) ²/Q_(high); Q_(low)/Q_(high) ²; Q_(low) ²/Q_(high) ²;        Q_(low) ²/Q_(high) ².

In particular preferred embodiments of the invention, the correctingfunction is of the form:$\frac{Q_{low}^{m}}{Q_{high}^{m}} = {{B_{1}Q_{low}^{s}} + {B_{2}Q_{high}^{s}} + {B_{3}Q_{low}^{s2}} + {B_{4}Q_{high}^{s2}} + {B_{5}Q_{low}^{s}Q_{high}^{s}} + {B_{6}Q_{low}^{s2}Q_{high}^{s}} + {B_{7}Q_{low}^{s}Q_{high}^{s2}} + {B_{8}\frac{Q_{low}^{s}}{Q_{high}^{s}}} + {B_{9}\frac{Q_{low}^{s2}}{Q_{high}^{s}}} + {B_{10}\frac{Q_{low}^{s}}{Q_{high}^{s2}}} + {B_{11}\lbrack \frac{Q_{low}^{s}}{Q_{high}^{s}} \rbrack}^{2} + B_{0}}$

The above-defined method can be adequate for many cases. However, in ageneralized version of the method the above-mentioned correctingfunction is accompanied by a further correcting function beingdetermined based on the sets of responses and being a functionalrelationship between responses of the slave instrument (Q_(low) ^(s) orQ_(high) ^(s)) and related responses (Q_(low) ^(m) or Q_(high) ^(m)) ofthe master instrument. Thus, the method preferably comprisesdetermination of a second set of correcting coefficdents (α; β).

Experience has shown that in some cases the further correcting functionmay improve the correction.

Preferably and typically, the further correcting function is afunctional relationship between a high energy response of the slaveinstrument (Q_(high) ^(s)) and the related high energy response(Q_(high) ^(m)) of the master instrument. Furthermore, it is preferredthat the further correcting function is determined by use of univariatelinear regression.

In accordance with preferred embodiments of the present invention thefurther correcting function is preferably of the form Q_(high)^(m)=α·Q_(high) ^(s)+β.

It is preferred that the set of responses for the master instrument andthe set of responses for the slave instrument each comprises one pair ofrelated responses for each stable object comprised in the plurality ofstable objects.

In many practical implementations of the method the related responsesare advantageously obtained based on measuring on objects beingconveyed.

In cases where the detector or detectors used for providing theresponses is/are sufficiently stable in time in the sense that it is notnecessary to take measures to eliminate for instance detector drift inorder to maintain the overall accuracy of the measurement, it might notbe necessary to apply the method to any transformed responses. In suchcases it is preferred that each of the responses (Q) is an intensity(I), if necessary corrected with respect to a variable parameter, e.g.dark current of the detectors. Thus, it might be preferred to correctthe raw intensity with respect to the dark current in order to increasethe stability of the responses by compensating for instability in thedetector.

Such intensities are especially useful in situations where theintensities vary linearly or substantially linearly with physicalproperties reflected, which in particular is the situation where themeasured absorption characteristics of an object varies over a narrowinterval.

To compensate for further instabilities, e.g. due to radiation sourceinstability, it is typically preferred that each of the responses is atransmittance (T) being derived from intensity as a ratio betweenintensity resulting from measuring on an object and reference intensity.Of course, such transmittances may also be preferred in general.

In preferred embodiments a linearization of transmittance is applied. Insuch and of course other embodiments as well, it is preferred that eachof the responses is an absorbance being defined as the negativelogarithm to a transmittance (A=−log(T)) such as logarithm base 10, thenatural logarithm, or any other logarithmic function.

In particular preferred embodiments of the present invention, theresponses for both the master and the slave instruments are absorbancesbeing determined by calculating$A_{low} = {{- {\log_{10}\lbrack \frac{{I_{sample}({low})} - {I_{dark}({low})}}{{I_{air}({low})} - {I_{dark}({low})}} \rbrack}}{\quad\quad}{and}}$$A_{high} = {- {\log_{10}\lbrack \frac{{I_{sample}({high})} - {I_{dark}({high})}}{{I_{air}({high})} - {I_{dark}({high})}} \rbrack}}$wherein the intensities (I) are obtained in a measuring region of themaster instrument respectively the slave instrument by:

-   -   exposing the object in the measuring region to low and high        X-ray energies and detecting with detectors the intensities        I_(sample)(Iow) and I_(sample)(high) respectively    -   detecting the intensities I_(dark)(low) and I_(dark)(high) from        said detectors when no radiation reaches them; and    -   exposing said detectors to the low and high X-ray energies        signals when no object is present in the measuring region and        detecting I_(air)(low) and I_(air)(high).

In other preferred embodiments, each of the responses is selected to bea reflectance (R) expressing the reflectance from the surface of theobject. The measured reflectance being useful in situations where theobject to measured has such a nature that the properties to be measuredis expressed by the reflectance of the object. It is contemplated thatthe reflectance covers surface reflectance of the object as well asreflectance in general of the object.

In preferred embodiments using reflectance it is preferred that thereflectance is linearized. In such embodiments the reflectance (R) islinearized, preferably by using the Kubelka-Munk transformation(K/S=(1−R)/2R).

The present invention relates in a second aspect to a method ofcorrecting responses representing measurements performed with a slaveinstrument, said method comprising for an object

-   -   determining based on measurements with the slave instrument a        pair of related responses (Q_(low) ^(s) and Q_(high) ^(s)),    -   determining the ratio [Q_(low)/Q_(high)]^(corr) by a correcting        function being a functional relationship between a ratio of        related responses of the master instrument and a sum of a        plurality of terms, each term being a product of a correcting        coefficient (B_(I)) and powers of related responses (Q_(low)        ^(s) and Q_(high) ^(s)) of the slave instrument wherein each        response being raised to a power being a positive or negative        real number, or zero,    -   providing Q_(high) ^(corr) either by assuming that Q_(high)        ^(corr) is substantially equal to Q_(high) ^(s) or by use of a        further correcting function correlating Q_(high) ^(corr) with        Q_(high) ^(s); and    -   calculating Q_(low) ^(corr) as Q_(high)        ^(corr)*[Q_(low)/Q_(high)]^(corr);        thereby providing a set of corrected responses.

Thus, in accordance with the invention, the method of correctingresponses comprises preferably three operations, namely determination ofa ratio of responses, determining one of the responses of the ratio ofresponses and finally multiplying said one of the responses on the ratiodetermined. It should be noted, that the assumption that Q_(high)^(corr) is substantially equal to Q_(high) ^(s) can be construed asbeing a further correcting function (of the form Q_(high)^(corr)=Q_(high) ^(s)) also, but is not termed so in order to ease thefollowing discussion only.

When a further correcting function is utilised, this further correctingfunction is preferably of the form Q_(high) ^(corr)=α·Q_(high) ^(s)+β.It is contemplated that one or both of the coefficients (α, β) andespecially β can be determined or selected to be equal to zero.

It is in general preferred that the correcting function comprises termsof the following form Q_(low) ^(n1)*Q_(high) ^(m1) wherein n1 and m2 arereal numbers and/or integers, and wherein n1 is positive. In accordancewith preferred and practical very useful embodiments of the presentinvention it is preferred that the correcting function comprises thefollowing terms: Q_(low), Q_(high), Q_(low) ², Q_(high) ² andQ_(low)/Q_(high). In order to gain a higher accuracy in the correctingthe correcting function may preferably comprise more terms such that thecorrecting function preferably comprises the following terms:Q_(low)*Q_(high); Q_(low) ²*Q_(high); Q_(low)*Q_(high) ²; Q_(low)²/Q_(high); Q_(low)/Q_(high) ²; Q_(low) ²/Q_(high) ²; Q_(low) ²/Q_(high)².

In particular preferred embodiments of the second aspect of the presentinvention the correcting function is of the form:$( \frac{Q_{low}}{Q_{high}} )^{corr} = {{B_{1}Q_{low}^{s}} + {B_{2}Q_{high}^{s}} + {B_{3}Q_{low}^{s2}} + {B_{4}Q_{high}^{s2}} + {B_{5}Q_{low}^{s}Q_{high}^{s}} + {B_{6}Q_{low}^{s2}Q_{high}^{2}} + {B_{7}Q_{low}^{s}Q_{high}^{s2}} + {B_{8}\frac{Q_{low}^{s}}{Q_{high}^{s}}} + {B_{9}\frac{Q_{low}^{s2}}{Q_{high}^{s}}} + {B_{10}\frac{Q_{low}^{s}}{Q_{high}^{s2}}} + {B_{11}\lbrack \frac{Q_{low}^{s}}{Q_{high}^{s}} \rbrack}^{2} + B_{0}}$

Wherein the B's preferably are constants being in general real numbers.

In preferred embodiments and as disclosed in relation to the firstaspect of the present invention each of the responses (Q) is in somesituations preferred to be an intensity (I), if necessary corrected withrespect to the dark current of the detectors. Such intensity mayadvantageously be transformed into a transmittance (T) being derivedfrom intensity as a ratio between intensity resultingfrom measuring onan object and a reference intensity.

In order to, for instance, linearize the responses, it might bepreferred that each of responses is an absorbance being defined as thenegative logarithm to a transmittance (A=−log(T)) such as logarithm base10, the natural logarithm, or any other logarithmic function.

In particular preferred embodiments the responses are absorbances beingdetermined by calculating$A_{low} = {{- {\log_{10}\lbrack \frac{{I_{sample}({low})} - {I_{dark}({low})}}{{I_{air}({low})} - {I_{dark}({low})}} \rbrack}}{\quad\quad}{and}}$$A_{high} = {- {\log_{10}\lbrack \frac{{I_{sample}({high})} - {I_{dark}({high})}}{{I_{air}({high})} - {I_{dark}({high})}} \rbrack}}$wherein the intensities (I) are obtained in a measuring region of theslave instrument by:

-   -   exposing an object in the measuring region to low and high X-ray        energies and detecting with detectors the intensities        I_(sample)(low) and I_(sample)(high) respectively    -   detecting with the detectors the intensities I_(dark)(low) and        I_(dark)(high) from said detectors when no radiation reaches        them; and    -   exposing said detectors to the low and high X-ray energies        signals when no object is present in the measuring region and        detecting I_(air)(low) and I_(air)(high).

Also in this aspect of the present invention it may be preferred thateach of the responses is a reflectance (R) expressing the reflectancefrom the surface of the object and the reflectance (R) may preferablyand advantageously be linearized, preferably by using the Kubelka-Munktransformation (K/S=(1−R)/2R).

The correcting function and the further correcting function utilized inthe second aspect of the present invention are preferably determined bythe method according to the first aspect of the present invention.

The present invention relates in a third aspect to a method ofdetermining a physical quantity for an object by a slave instrument. Inthis aspect the method comprises preferably

-   -   determining for the object corrected high and low energy        responses (Q_(high) ^(corr) and Q_(low) ^(corr)) by utilizing        the method according to the second aspect of the present        invention,    -   determining the physical quantity by applying on said corrected        responses a calibrated functional relationship between Q_(high)        ^(corr) and Q_(low) ^(corr) and a physical quantity.

In accordance with the third aspect, it is preferred that the calibratedfunctional relationship being a functional relationship between aphysical quantity (such as the content of a specific constituent e.g.fat and meat), and a sum of a plurality of terms, each term being aproduct of a calibration coefficient (B_(I)) and powers of relatedresponses (Q_(low) ^(s) and Q_(high) ^(s)) wherein each response beingraised to a power being a positive or negative real number, or zero.

In preferred embodiments of third aspect of the present invention, thecalibrated functional relationship comprises terms being of the form:Q_(low) ^(n1)*Q_(high) ^(m1) wherein n1 and m2 are real numbers and/orintegers, and wherein n1 is positive. In order to for instance increasethe accuracy of the calibrated functional relationship this relationshipmay preferably comprises terms being of the form: Q_(low), Q_(high),Q_(low) ², Q_(high) ² and Q_(low)/Q_(high), or preferably comprisesterms of the form: Q_(low)*Q_(high); Q_(low) ²*Q_(high);Q_(low)*Q_(high) ²; Q_(low) ²/Q_(high); Q_(low)/Q_(high) ²; Q_(low)²/Q_(high) ²; Q_(low) ²/Q_(high) ².

In particular preferred embodiments according to the third aspect of thepresent invention the calibrated functional relationship is of the form:${F(Q)} = {{B_{1}Q_{low}^{s}} + {B_{2}Q_{high}^{s}} + {B_{3}Q_{low}^{s2}} + {B_{4}Q_{high}^{s2}} + {B_{5}Q_{low}^{s}Q_{high}^{s}} + {B_{6}Q_{low}^{s2}Q_{high}^{s}} + {B_{7}Q_{low}^{s}Q_{high}^{s2}} + {B_{8}\frac{Q_{low}^{s}}{Q_{high}^{s}}} + {B_{9}\frac{Q_{low}^{s2}}{Q_{high}^{s}}} + {B_{10}\frac{Q_{low}^{s}}{Q_{high}^{s2}}} + {B_{11}\lbrack \frac{Q_{low}^{s}}{Q_{high}^{s}} \rbrack}^{2} + B_{0}}$

It may furthermore be preferred that the calibration model is obtainedby exposing the master instrument, such as an instrument having carriedout the method according to the first aspect of the present invention,to a plurality of well-defined objects.

Typically and preferably, well-defined objects are defined in the sensethat the physical properties of the objects have been established by achemical process, such as an officially recognized reference method forthe determination of the requested physical properties.

In preferred embodiments and as disclosed in relation to the otheraspect of the present invention, each of the responses (Q) is preferablyeither:

-   -   an intensity (I), if necessary corrected with respect to dark        current of the detectors;    -   a transmittance (T) being derived from intensity as a ratio        between intensity resulting from measuring on an object and a        reference intensity;    -   an absorbance being defined as the negative logarithm to a        transmittance (A=−log(T)) such as logarithm base 10, the natural        logarithm, or any other logarithmic function; or    -   a reflectance (R) expressing the reflectance from the surface of        the object, the reflectance (R) is preferably linearized using        the Kubelka-Munk transform (K/S=(1−R)/2R).

In particular preferred embodiments according to the third aspect of thepresent invention where the responses are absorbance, such absorbancesare preferably being determined by calculating$A_{low} = {{- {\log_{10}\lbrack \frac{{I_{sample}({low})} - {I_{dark}({low})}}{{I_{air}({low})} - {I_{dark}({low})}} \rbrack}}{\quad\quad}{and}}$$A_{high} = {- {\log_{10}\lbrack \frac{{I_{sample}({high})} - {I_{dark}({high})}}{{I_{air}({high})} - {I_{dark}({high})}} \rbrack}}$wherein the intensities (I) are obtained in a measuring region of theslave instrument by:

-   -   exposing an object in the measuring region to low and high X-ray        energies and detecting with detectors the intensities        I_(sample)(low) and I_(sample)(high) respectively    -   detecting with the detectors the intensities I_(dark)(low) and        I_(dark)(high) from said detectors when no radiation reaches        them; and    -   exposing said detectors to the low and high X-ray energies        signals when no object is present in the measuring region and        detecting I_(air)(low) and I_(air)(high).

In a fourth aspect the present invention relates to a method of using aslave instrument for determining physical quantities. Such physicalquantities are for instance: preferably the fat content of an object,which object is for instance food or feed, and the quantities arepreferably determined by use of dual X-ray radiation. In accordanceherewith, the method comprises preferably:

-   -   scanning substantially all or all of the object by X-ray beams        having at least two energy levels, including a low level and a        level being higher relatively thereto,    -   detecting the X-ray beams having passed through the object for a        plurality of areas of the object;    -   for each area of the object        -   determining the object's response (Q_(low)) at the low            energy level and the object's response (Q_(high)) at the            high energy level,        -   correcting the responses so determined preferably by            utilizing the correcting method according to the second            aspect of the present invention, and        -   determining the physical property preferably by utilizing            the method according the third aspect of the present            invention.

In a sixth aspect of the present invention, the invention relates to adata processing system for providing a correction for a slaveinstrument. Such a system utilizes preferably sets of responses beingbased on detecting attenuation and/or reflection and/or scatter ofelectromagnetic radiation, in particular X-ray, in/from a object exposedto said electromagnetic radiation in at least two spectral ranges. Theset of responses comprises preferably one or more pair of relatedresponses (Q_(low) ^(s) and Q_(high) ^(s)) representing measurementsperformed with a slave instrument and a set of responses comprising oneor more pair of related responses (Q_(low) ^(m) and Q_(high) ^(m)representing measurements performed with a master instrument. Theseresponses being preferably obtained for a plurality of stable objectsand

-   -   to each pair of related responses of the slave instrument        corresponds a pair of related responses of the master        instrument,    -   and to each element in each pair of responses of the slave        instrument corresponds an element in the corresponding pair of        responses of the master instrument.

In accordance with the sixth aspect the data processing system comprisespreferably

-   -   means for accessing memory means wherein the responses (Q_(low)        ^(m) and Q_(high) ^(m)) of the master instrument and/or the        responses (Q_(low) ^(s) and Q_(high) ^(s)) of the slave        instrument are stored,    -   means, such as processor means, for determining based on the        sets of responses a correcting function being a functional        relationship between a ratio of related responses of the master        instrument and a sum of a plurality of terms, each term being a        product of a correcting coefficient (B_(i)) and powers of        related responses (Q_(low) ^(s) and Q_(high) ^(s) of the slave        instrument wherein each response being raised to a power being a        positive or negative real number, or zero, thereby determining a        first set of correcting coefficients (B₀; B₁; B₂ . . . ) being        multiplied on each of the terms,        -   means for storing the first set of correction coefficients            (B₀; B₁; B₂ . . . ).

Data processing systems of the sixth aspect of the invention comprisepreferably means for determining a further correcting function being afunctional relationship between a high energy response of the slaveinstrument (Q_(high) ^(s)) and related high energy response (Q_(high)^(m)) of the master instrument, thereby enabling the system todetermining a second set of correcting coefficients (α; β).

In accordance with preferred embodiments of the data processing systemaccording to the present invention, and as disclosed in connection withthe other embodiments of the invention, it is preferred that each of theresponses (Q) is either:

-   -   an intensity (I), if necessary corrected with respect to dark        current of the detectors;    -   a transmittance (T) being derived from intensity as a ratio        between intensity resulting from measuring on an object and        reference intensity;    -   an absorbance being defined as the negative logarithm to a        transmittance (A=−log(T)) such as logarithm base 10, the natural        logarithm, or any other logarithmic function; or    -   a reflectance (R) expressing the reflectance from the surface of        the object, the reflectance (R) is preferably linearized using        the Kubelka-Munk transform (K/S=(1−R)/2R).

In particular preferred embodiments of the data processing systemaccording to the present invention, in case the responses areabsorbances, the absorbances being preferably determined by calculating$A_{low} = {{- {\log_{10}\lbrack \frac{{I_{sample}({low})} - {I_{dark}({low})}}{{I_{air}({low})} - {I_{dark}({low})}} \rbrack}}{\quad\quad}{and}}$$A_{high} = {- {\log_{10}\lbrack \frac{{I_{sample}({high})} - {I_{dark}({high})}}{{I_{air}({high})} - {I_{dark}({high})}} \rbrack}}$wherein the intensities (I) are obtained in a measuring region of theslave instrument by:

-   -   exposing an object in the measuring region to low and high X-ray        energies and detecting with detectors the intensities        I_(sample)(low) and I_(sample)(high) respectively    -   detecting with the detectors the intensities I_(dark)(low) and        I_(dark)(high) from said detectors when no radiation reaches        them; and    -   exposing said detectors to the low and high X-ray energies        signals when no object is present in the measuring region and        detecting I_(air)(low) and I_(air)(high).

In a seventh aspect, the invention relates to a correcting systemcomprising a slave instrument for obtaining responses and a dataprocessing system for correcting the responses, the responsesrepresenting measurement performed with the slave instruments and theresponses being based on detecting by the slave instrument attenuationand/or reflection and/or scatter of electromagnetic radiation, inparticular X-ray, in/from a object exposed to said electromagneticradiation in at least two spectral ranges, the set of responsescomprises one or more pair of related responses (Q_(low) ^(s) andQ_(high) ^(s)). In accordance herewith, the correcting system comprisespreferably

-   -   processor means for determining the one or more pair of related        responses (Q_(low) ^(s) and Q_(high) ^(s)) based on measurement        on an object with the slave instrument,    -   means comprising processor means adapted to perform a correction        of responses by utilizing a correcting according to the second        aspect of the present invention, said processor means comprises        -   means for accessing memory means storing a first set of            correction coefficients (B₀; B₁; B₂ . . . )        -   processor means for determining the ratio            [Q_(low)/Q_(high)]^(corr) by the correcting function;        -   processor means for determining the corrected high energy            response Q_(high) ^(corr) by the further correcting            function; and        -   processor means for determining the corrected low energy            response Q_(low) ^(corr) by multiplying [QbW Q_(high])            ^(corr) by Q_(high) ^(corr).

Also in this aspect of the invention, and as disclosed in connectionwith the other aspects of the invention, each of the responses (Q) ispreferably either:

-   -   an intensity (I), if necessary corrected with respect to dark        current of the detectors;    -   a transmittance (T) being derived from intensity as a ratio        between intensity resulting from measuring on an object and        reference intensity;    -   an absorbance being defined as the negative logarithm to a        transmittance (A=−log(T)) such as logarithm base 10, the natural        logarithm, or any other logarithmic function; or    -   a reflectance (R) expressing the reflectance from the surface of        the object, the reflectance (R) is preferably linearized using        the Kubelka-Munk transform (K/S=(1−R)/2R).

Preferably, the system according to the seventh aspect comprises storagemeans wherein a set of responses (Q_(low) ^(m) and Q_(high) ^(m)) for aset of stable objects measured on a master instrument are stored and/orstorage means wherein the first set of correction coefficients (B₀; B₁;B₂ . . . ) and/or the further correcting function is/are stored.

In an eighth aspect, the present invention relates to a dual X-rayinstrument comprising a system according to the seventh aspect beingadapted to carry out a method according to the first aspect of theinvention.

In a ninth aspect, the present invention relates to a set of objectscomprising one or more stable objects for, or used during, carrying outone or more of the methods according to the present invention.Preferably, each of such objects being characterized by being composedby at least two different chemical compositions which are substantiallystable and each stable object is having response, such as absorbance,properties which are similar to the response, such as absorbance,properties of an object subjected to the method according to the secondaspect of the present invention.

In accordance with the ninth aspect, it is preferred that for each ofthe stable objects a first member of the at least two different chemicalcompositions is one having X-ray response properties, such as absorbanceproperties, similar to adipose tissue, and a second member of the atleast two different chemical compositions is one having X-ray response,such as absorbance, properties similar to muscle tissue.

In preferred embodiments of present invention, the set of stable objectscomprises preferably a plurality of stable objects having varyingthickness and/or areal density. The plurality of stable objects mayadvantageously be integrated into a single stepped item.

Preferably, each object comprised in the set of objects is stable in thesense that the X-ray response, such as absorption, properties of theobject does not change more than 0.1%, such as no more than 0.01%, suchas no more than 0,001% within at least 10 days, such as at least 1month, preferably at least 1 year.

Preferably, the number of stable objects comprises in the set of stableobjects are at least 8, such as at least 12, preferably at least 15, oreven at least 20, such as at least 26.

In the following a particular preferred embodiment of the presentinvention will be presented as non-limiting example with reference tothe accompanying figures, in which:

FIG. 1 shows a schematic diagram of an instrument incorporating meansfor carrying out a method according to the invention.

FIG. 2 shows a perspective view of an embodiment of the instrument inFIG. 1.

FIG. 3 shows an alternative spectrum of X-ray sources simulating twosources by use of one source and a combination of two filters.

FIG. 4 shows a typical meat sample in a plastic container.

FIG. 5 shows a typical low energy X-ray transmission image of a meatsample as shown in FIG. 4.

FIG. 6 shows a typical high energy X-ray transmission image of the samemeat sample.

FIG. 7 is an image illustrating a calculated areal density for eachindividual pixel.

FIG. 8 is an image illustrating a calculated fat content for eachindividual pixel.

FIG. 9 is an image illustrating a calculated “fat map” for a meat sampleof 36% fat.

FIG. 10 shows an embodiment of an integrated standardization object.

FIG. 11 shows an embodiment of individual steps of an integratedstandardization object.

FIG. 12 shows a second embodiment of an integrated standardizationobject

FIG. 13 shows a further embodiment of a number of steps and sections ofan integrated standardization object.

FIG. 14 shows a flow diagram illustrating the measuring process with amaster instrument.

FIG. 15 shows a flow diagram illustrating the standardisation process.

FIG. 16 shows a flow diagram illustrating the new measurement processusing a standardized slave.

FIG. 17 shows a plot of ratios of non-standardised absorbances obtainedwith four non-standardised instruments against ratios of absorbancesobtained with a master instrument,

FIG. 18 shows a plot of ratios of standardised absorbances obtained withfour standardised instruments against ratios of absorbances obtainedwith a master instrument,

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE PRESENT INVENTION

The present invention may be applied for instruments of the kindmeasuring absorbances, in a medium, of an electromagnetic radiation inat least two spectral ranges, which instrument is calibrated by use of amultivariate regression method. Such instruments may be spectralIR-instruments. However, the present invention has proved to bespecifically useful for Dual X-ray analysis.

Description of the Equipment Used

The following description discloses as an example a preferred embodimentof an instrument for which the present invention is specificallyintended. The instrument uses two X-ray sources. The instrument isdesigned for being installed in relation to a production line in aslaughterhouse. FIG. 1 shows a schematic diagram of an embodiment of ameasurement system for a determination of the fat content in meat. FIG.2 is a perspective illustration of the presently preferred X-rayinstrument. FIG. 2 shows only the active operating portions of the X-rayequipment. For purpose of clarity, all protective shielding or screeningand all casings are deleted from the drawing. The equipment comprises oris located in close relation to a conveyor 10. Two X-ray sources 12, 14are arranged above the conveyor 10. From the two sources 12, 14 X-raybeams 16, 18 are directed towards detectors 22, 24 arranged below theconveyor. The conveyor may be split into two separate conveyors spacedto allow free pass of the X-rays and to leave an open space for locationof detectors 22, 24. Alternatively the conveyor belt should be made froma material showing a low absorbance of X-rays, e.g. polyurethane orpolypropylene. The food or feed to be measured is arranged in an opencontainer or box 20, preferably also composed by a material showing lowabsorbance of X-rays. Alternatively the medium such as a food productmight be arranged directly on a conveyor belt. In a further alternativearrangement the X-ray sources could be located below the conveyor andthe detectors above the conveyor.

The presently preferred equipment used in the present example consistsof two constant potential X-ray sources 12, 14, one at low energy (e.g.62 kV/5.5 mA) and another at high energy (e.g. 120 kV/3.0 mA), both withan appropriate filtration (e.g. using 0.25 and 1.75 mm of copper,respectively) narrowing the spectral range of the radiation emitted fromthe polychromatic sources. The two sources are spatially separated toavoid interference between them, i.e. to avoid that radiation from onesource is detected as if it originated from the other. The radiationfrom either source is collimated by a lead collimator. In this way twofan-shaped beams of X-rays 16, 18 are directed through container 20comprising a sample or batch of the food or feed product towardsdetectors 22, 24, e.g. Hamamatsu C 7390. Alternatively the meat lumpsmay be arranged loosely on a conveyor band.

Further, the two separate sources may be replaced by a combination ofone source and two filters emitting a low energy and a high energy beam.The resulting source spectra are shown in FIG. 3. However the preferredembodiment applies two separate sources 12, 14 driven by separate powersupplies 13, 37.

Each of the two X-ray sources 12, 14 is associated with an array ofdetectors 22, 24 covered with a scintillating layer converting thetransmitted radiation into visible light that can be measured by thedetectors 22, 24. The scintillating layer may consist of e.g. cadmiumtelluride, mercury iodide, cesium iodide (CsI), gadolinium oxysulphide(Gd₂O₂S), or yttrium oxysulphide (Y₂O₂S), and/or CdWO₄, preferably dopedin order to reduce the after-glow effect. The pixels used in thepresently preferred embodiment have the dimensions 1.6×1.3 mm² and arearranged as an array of 384 pixels with a pitch of 1.6 mm. Thesedimensions are only stated as an example. Other dimensions may beapplied. The pixels convert the amount of transmitted light intoanalogue signals' that are passed through cables 27, 28 to ananalogue-to-digital converter 34, which is connected through cable 35 toa computing means 38 capable of performing the successive calculations.

A monitor 42 may be connected through cable 40 to the computing means toshow results or details of the operation. The computing means 38 mayinclude means for controlling the supply of power through means 36, 37,26 and 25, 13, 15 to the X ray sources 12, 14. The monitor 42 and thecomputing means 38 may comprise a Personal Computer, preferablyincluding at least one Pentium processor and/or a number of digitalsignal processors.

The operational speed of the conveyor is preferably substantiallyconstant. The items, motor 30; control box 33, and cables 32, 39, shownby phantom lines in FIG. 1, indicate that the operation of the conveyoroptionally may be controlled by the computing means 38. The conveyor mayinclude position measuring means, e.g. an encoder installed on aconveyor driving shaft. Alternative means may be a laser or radardetection or marks on the conveyor belt. It is essential to the presentmethod that the data representing the two X-ray images can besynchronised. Such synchronisation may however be obtained in many ways,including mathematical post-processing of the images.

Operation of the Instrument During a Normal Measurement:

A container 20, e.g. as shown in FIG. 4, comprising e.g. meat trimmingsfrom a cutting section of the slaughterhouse, is received on theconveyor 10. The container is moved with a fairly constant speed of e.g.about 5-100 cm per second, such as 10-50 cm, e.g. 30 cm per second pastthe fan shaped beams 16, 18 and the arrays of detectors 22, 24 in acontrolled manner in order to generate two “images” of the absorbancesin the sample or batch, one at a low X-ray energy (shown in FIG. 5) andanother at a high energy (shown in FIG. 6). All data representing thetwo images are stored in the computer 38.

Treatment of the Collected Data from a Master Instrument:

FIG. 14 represents a flow chart illustrating the measurement and datatreatment in a master instrument. As stated above, data representing twoX-ray images of (FIGS. 5, 6) of each container (FIG. 4), comprising abatch of food or feed e.g. meat, are obtained. The signals at the pixelsare I_(low) and I_(high) at low and high X-ray energies, respectively,(110, 112 in FIG. 14). Furthermore, the so-called “dark signals” (i.e.the signal from the detectors when no radiation reaches them),I_(dark)(low) and I_(dark)(high), and the “air signals” (i.e. the signalfrom the detectors when no sample is present in the measuring region),I_(air)(low) and I_(air)(high), are collected for each pixel at bothX-ray energies (102 in FIG. 14). Preferably these data are collectedrepetitively in the intervals between the passage/passing of meatcontainers, i.e. the dark signals and air signals are measuredrepetitively, e.g. at regular intervals during a day to adjust for anydrift of instrument performance.

Now referring to 114 in FIG. 14, these signals are transformed intoabsorbance units by using the following formulas: $\begin{matrix}{A_{low} = {- {\log_{10}\lbrack \frac{{I_{sample}({low})} - {I_{dark}({low})}}{{I_{air}({low})} - {I_{dark}({low})}} \rbrack}}} & ( {1a} ) \\{A_{high} = {- {\log_{10}\lbrack \frac{{I_{sample}({high})} - {I_{dark}({high})}}{{I_{air}({high})} - {I_{dark}({high})}} \rbrack}}} & ( {1b} )\end{matrix}$

If the instrument were a calibrated master instrument the areal density(FIG. 7) and fat content (FIG. 8, 9) of the measured medium could now becalculated from these absorbances by use of the fat calibration asdescribed in WO 01/29557 and shown schematically in box 116 in FIG. 14.

Description of the Method and Means According to the Present Invention:

A.: Description of the Standardisation Objects.

FIGS. 10-13 show various preferred embodiments of integratedstandardization objects. The present method requires a plurality ofstable objects, also called artificial samples due to the choice ofmaterial, which must be of a kind maintaining substantially constantabsorption properties for a long period, such as several years, contraryto the medium, such as meat, for which this method is specifically—butnot exclusively—intended. Preferably, the stable objects include anumber of combinations of two X-ray absorbers, having absorptioncharacteristics similar to the measured object, which in the presentexample is meat. Accordingly, in the present example, the two absorbersmust behave like adipose and muscle tissue. In the presently preferredembodiment blocks of polymethyl methacrylate 81 (similar to adiposetissue) and “plastic water” 82 (a polymer with absorptioncharacteristics similar to water, available from CIRS, Inc.) were used.Other alternatives, such as other purpose-made polymers made to resembleadipose and muscle tissue, could also be used. Liquid water (or ice) isanother substance highly resembling muscle tissue.

In the present example twenty-six samples consisting of variouscombinations of these materials 81 82 were generated (areal densitiesranging from approx. 1 to 22 g/cm²) and used in the standardisationprocedure.

In order to make the standardization process easy to perform it ispreferred that the whole number of different stable objects areintegrated into a single item, e.g. a stepped item, e.g. like astaircase 50 as shown in FIGS. 10 and 12. As shown in FIGS. 11 and 13each step 51, 52, 70, 71, . . . 79 may comprise one or two or an otherplurality of different layers 81, 82 of e.g. the polymethyl methacrylateand “plastic water. Further each step 51, 52, 70 may comprise severalsections 53, 54, 55, . . . 59, each having a specific combination oflayers 81, 82 of various thickness. Preferably, the differentcombinations are chosen to provide a range of absorptions andproperties, e.g. fat % similar to the absorptions and properties, e.g.fat %, in the media for which the instrument is intended.

Preferably, each section has the same size in the travel direction ofthe conveyor. Preferably, they also have the same size in a directionperpendicular to the travel direction and parallel to the conveyor belt.In other word the projection area on the generally horizontal plane ofthe conveyor belt of each section is the same in a preferred embodiment.

Each standardisation object is measured on a master instrument orstandardized slave instrument. Preferably, each standardization objectis marked by an identification code, such as a number. The measuredabsorbances and preferably the identification code are stored in amemory, which is accessible from a slave instrument, using thestandardization object.

B Standardization of a Slave Instrument

The standardisation procedure requires a set of aibsorbances, A_(low)^(m) and A_(high) ^(m), from a master instrument, and a set ofcorresponding absorbances, A_(low) ^(s) and A_(high) ^(s), from a slaveinstrument. These absorbances must originate from the same samples, e.g.a number of artificial standardisation samples, preferably being astandardization object as described above.

A presently preferred method according to the invention is shownschematically in the diagram FIG. 15. In step 202 I_(dark)(low) andI_(dark)(high), and I_(air)(low) and I_(air)(high), are collected foreach pixel at both X-ray energies. Preferably these data are collectedrepetitvely in the intervals between the passage/passing of meatcontainers, i.e. the dark signals and air signals are measuredrepetitively, e.g. at regular intervals during a day to adjust for anydrift of instrument performance.

In step 204 a standardization object 50 is arranged on the conveyor 10(shown in FIG. 1 and 2). The object is passed through the instrument inthe same manner as an ordinary object to be measured. The steps 200,202, 204, 206, 208, 210, 212, are the same as mentioned before regardingFIG. 14.

In the following step 214 average values A_(low) ^(s), A_(high) ^(s) arecalculated for each section 53, 54, 65, . . . 59, of the standardizationobject 50 measured on the slave instrument. The values are calculatedusing formula (1a) and (1b). The high and low energy values arecoordinated, i.e. the values belonging to the same section (53, 54, 55,. . . 59,) are matched. The corresponding values A_(low) ^(m), A_(high)^(m), measured on a master instrument are read from a memory.

The following final steps listed in box 216 are then required to obtainan acceptable standardisation of the instruments:

1. The coefficients (α and β) in the equation describing therelationship between A_(high) ^(m) and A_(high) ^(m) are determined byunivariate linear regression:A _(high) ^(m) =α·A _(high) ^(s)+β

This step may in some cases be superfluous as a may be almost equal to 1and 0 close to zero.

2. A functional relationship, f(A_(low) ^(s),A_(high) ^(s)), between theA_(low) ^(m)/A_(high) ^(m) ratio and various combinations of A_(low)^(s) and A_(high) ^(s) is established. The following linear combinationis preferred:$\frac{A_{low}^{m}}{A_{high}^{m}} = {{{B_{1}A_{low}^{s}} + {B_{2}A_{high}^{s}} + {B_{3}A_{low}^{s2}} + {B_{4}A_{high}^{s2}} + {B_{5}A_{low}^{s}A_{high}^{s}} + {B_{6}A_{low}^{s2}A_{high}^{s}} + {B_{7}A_{low}^{s}A_{high}^{s2}} + {B_{8}\frac{A_{low}^{s}}{A_{high}^{s}}} + {B_{9}\frac{A_{low}^{s2}}{A_{high}^{s}}} + {B_{10}\frac{A_{low}^{s}}{A_{high}^{s2}}} + {B_{11}\lbrack \frac{A_{low}^{s}}{A_{high}^{s}} \rbrack}^{2} + B_{0}} = {f( {A_{low}^{s},A_{high}^{s}} )}}$+B₈ Ajw+B₉ A₁W+BI SO.2+B₁ AI+Bo.=.(AsoWAsigh)

The coefficients, B₀ to B₁₁, are be determined e.g. by using PartialLeast Squares (PLS) regression. Alternatively other multivarialteregression methods may be used.

3. The coefficients, α, β, and B₀ to B₁₁, are saved in the instrument.They are the instrument specific standardisation (correction)coefficients.

C. Measuring an Unknown Meat Sample on the Standardized SlaveInstrument:

A presently preferred procedure for measuring a new meat sample on theslave instrument is illustrated in FIG. 16. A container (FIG. 4) isarranged on the conveyor 10. During the passage through the instrumentthe two X-ray beams pass through the meat, container bottom, conveyorbelt and reach the detectors 22, 24, generating signals representing thetwo images shown in FIGS. 5, 6. Data representing the intensitiesI_(low), I_(high) are stored temporarily. I_(dark) and I_(air) aremeasured regularly in step 312. Absorbances A_(low) ^(s), A_(high) ^(s)are calculated by use of formula (1a) and (1b). For each pixel—oralternatively a small group of neighboring pixels—two matching valuesA_(low) ^(s), A_(high) ^(s) are coordinated. So far the data treatmentis the same as shown in FIG. 14. According to the present invention thefollowing treatment is applied to the raw measurements, A_(low) ^(s) andA_(high) ^(s), from the slave instrument:

1. The corrected high energy absorption, A_(high) ^(corr), iscalculated:A _(high) ^(corr) =α·A _(high) ^(s)+βby using α and β determined as disclosed above in section C.

2. The corrected absorption ratio, [A_(low)/A_(high)]^(corr), iscalculated:$\lbrack \frac{A_{low}}{A_{high}} \rbrack^{corr} = {f( {A_{low}^{s},A_{high}^{s}} )}$where f is the function defined above in section C.

3. The corrected low energy absorption, A_(low) ^(corr), is calculated:$\lbrack \frac{A_{low}}{A_{high}} \rbrack^{corr} = {f( {A_{low}^{s},A_{high}^{s}} )}$

These corrected absorbances, A_(low) ^(corr) and A_(high) ^(corr), arehereafter used for predictive purposes, e.g. prediction of the fatcontent of a meat sample using a calibration model generated on themaster instrument (or any other instrument in the population ofstandardised instruments). This is indicated in the box 316, which isidentical to box 116 in FIG. 14.

The example presented below shows how the method may work in practice.

Meat Samples used for Exemplifying the Method According to theInvention:

86 samples consisting of minced pork, turkey, and beef meat wereprepared. These samples were frozen in blocks of varying heights (from10 to 200 mm, corresponding to areal densities from 1 to 21 g/cm²). Thefat content of these samples was determined using the fat referencemethod (SBR, Schmid-Bondzynski-Ratzlaff). It ranged from 2 to 73%. 44 ofthese samples were used for building calibration models while theremaining 42 samples were used for independent testing of thestandardisation method.

Description of the Measurements

The 26 artificial samples and the 86 meat samples were measured onequipment as described above. According to previous experience it isknown that particularly voltage changes in the low X-ray sources causeserious problems with the transferability of the calibrations.Therefore, the experiment was carried out five times with differentvoltage settings of the two energy sources, on different instruments.The following settings were used:

-   Instrument 1 (master): E_(low)=62 kV, E_(high)=120 kV-   Instrument 2 (slave): E_(low)=58 kV, E_(high)=100 kV-   Instrument 3 (slave): E_(low)=58 kV, E_(high)=110 kV-   Instrument 4 (slave): E₁₀=66 kV, E_(high)=110 kV-   Instrument 5 (slave): E_(low)=66 kV, E_(high)=100 kV.    Use of the Method

PLS calibration models for fat and areal density based oh 44 meatsamples were calculated on data from Instrument 1. This instrument istherefore regarded as the master instrument against which the so-calledslave instruments (Instruments 2 to 5) will be evaluated. Thecalibration models consist of linear combinations of various ratios andproducts of A_(low) and A_(high), such that the fat % in a specificspecific area or point of an object, above a specific single detectionelement, or alternatively a neighborhood of adjacent detection elements,such as four or nine, may be calculated as:Fat %=b ₀ +b ₁ *A _(low) +b ₂ *A _(high) +b ₃ *A _(low) ² +b ₄ *A_(high) ² +b ₅ *A _(low) /A _(high) +b ₆ *A _(low) *A _(high) +b ₇ *A_(low) ² *A _(high) +b ₈ *A _(low) *A _(high) ² +b ₉ *A _(low) *A_(high) ⁴ +b ₁₀ *A _(low) ² *A _(high) ⁴ +b ₁₁ *A _(low) ² /A _(high) +b₁₂ *A _(low) /A _(high) ² +b ₁₃ *A _(low) ² /A _(high) ² +b ₁₄ *A _(low)³ /A _(high) ² +b ₁₆ *A _(low) ⁴ /A _(high) ² +b ₁₆*1/A _(high) ⁴ +b ₁₇*A _(low) ⁴ /A _(high) ³ +b ₁₈ *A _(low) ³ /A _(high) ⁴ +b ₁₉ *A _(low)⁴ /A _(high) ⁴ + . . . +b _(p) *A _(low) ^(n1) /A _(high) ^(m1)wherein b₀, b₁, . . . b_(p) (some of them may be zero) are thecalibration coefficients determined through multivariate calibration.Typically, the series is truncated so as to contain only term up topower two, such as power three, preferably power four of A.

It is contemplated that the expected accuracy of a calibrated instrumentagainst the reference method (expressed as the Root Mean Square Error ofPrediction, RMSEP) is better than 1% for the fat determination andapprox 0.1 g/cm² for the areal density determination.

The A_(low)/A_(high) ratio is the parameter that is most sensitive towhether the instrument is standardised or not. This is of majorimportance, since this ratio is one of the major contributors to thecalibration model for fat. In FIG. 17 this ratio for the 86 meat samplesmeasured on the master instrument is plotted against thenon-standardised ratios for the slave instruments. If no standardisationproblems existed, the points should be close to the straight lineindicated in the figure. This is, however, far from true: especiallyInstrument 5 shows large errors. A simple slope and intercept correctionof this error will not help the problem completely, as the points, apartfrom showing a large systematic error, are also scattered along animaginary line passing through the cloud of points. This is the reasonwhy eleven or more terms are required in f(A_(low) ^(s),A_(high) ^(s)).

After calculation of the Instrument dependent standardisation(correction) coefficients; α, β, and B₀ to B₁₁, for Instrument 2 to 5from the data obtained on the 26 artificial samples, the absorbances ofthe 86 meat samples were corrected using these coefficients. Thisresulted in a set of corrected ratios, [A_(low)/A_(high)]^(corr), thatare plotted in FIG. 18. The ratios are now very close to the line,indicating that the ratio is independent of the instrument from which itoriginated, which means that calibration models can be transferredbetween instruments.

The result of various attempts to use the calibration models based ondata from the master (Instrument 1) are presented in Table A. Firstly,the calibration models for fat and areal density were applied to theraw, non-standardised data from the 42 independent test meat samples(corresponding to the data presented in FIG. 17). As is evident fromcolumn two and four of Table A, this results in very large andunacceptable prediction error. When standardisation is applied(corresponding to the data presented in FIG. 18), on the other hand, theprediction errors for the slaves (Instruments 2 to 5) cannot bedistinguished from the prediction error for the master (Instrument 1).This can be seen in columns three and five of Table A. TABLE A Theprediction error is stated in terms of the Root Mean Square Error ofPrediction (RMSEP) Non- Non- standardised Sandardised standardisedSandardised fat fat areal density areal density prediction predictionprediction prediction Instrument error (%) error (%) error (g/cm²) error(g/cm²) 1 master 0.66 0.66 0.10 0.10 2 slave 4.56 1.06 0.43 0.12 3 slave20.89 0.90 0.32 0.12 4 slave 38.08 0.72 0.19 0.11 5 slave 54.07 1.150.09 0.11Comments

The example given above thus shows the advantages of using the describedmethod for standardising an X-ray instrument. The major advantage liestypically in the fact that it is possible to use stable artificialsamples with well-defined absorption characteristics for obtainingstandardised fat and areal density predictions instead of having toperform a labour intensive and expensive calibration procedure for everynew instrument or every time an instrument is modified, e.g. byreplacing a defect X-ray source or detector.

While a single particular embodiment of the invention has beenmentioned, it will be understood, of course, that the invention is notlimited thereto since many modifications may be made. It is contemplatedthat it will be useful for other kinds of electromagnetic radiation aswell, e.g. Infrared light. It is, therefore, contemplated to cover bythe appended claims any such modifications as fall within the truespirit and scope of the invention.

1. A method of providing a correction for a slave instrument, the slaveinstrument measuring properties of an object by exposing the object toelectromagnetic radiation in at least two spectral ranges and obtainingone or more object responses thereto, the responses being based ondetecting at least one of attenuation, reflection and scattering of theelectromagnetic radiation in or from the object by use of one or moredetectors, the responses obtained in a form where they expressproperties either directly or via a transformation, said method ofcorrection comprising: obtaining, for a plurality of stable objects, aset of responses comprising one or more pairs of related responses(Q_(low) ^(s) and Q_(high) ^(s)) representing measurements in the atleast two spectral ranges performed with the slave instrument and a setof responses, comprising one or more pairs of related responses (Q_(low)^(m) and Q_(high) ^(m)) representing measurements in the at least twospectral ranges performed with a master instrument; wherein a pair ofrelated responses (Q_(low) ^(m) and Q_(high) ^(m)) of the masterinstrument corresponds to each pair of related responses (Q_(low) ^(s)and Q_(high) ^(s)) of the slave instrument, wherein each element in thecorresponding pair of responses (Q_(low) ^(m) and Q_(high) ^(m)) of themaster instrument corresponds to an element in each pair of responses(Q_(low) ^(s) and Q_(high) ^(s)) of the slave instrument; determining,based on the sets of responses, a correcting function, the correctingfunction being a functional relationship between a ratio of relatedresponses of the master instrument and a sum of a plurality of terms,each term being a product of a correcting coefficient (B_(i)) and powersof related responses (Q_(low) ^(s) and Q_(high) ^(s)) of the slaveinstrument, wherein each response is raised to a power being a positiveor negative real number, or zero, thereby determining a first set ofcorrecting coefficients (B₀; B₁; B₂ . . . ) being multiplied byrespective of each of the terms; and storing the first set of correctingcoefficients (B₀; B₁; B₂ . . . ) in a memory means included in oradapted for communication with a data processing unit included in oradapted for communication with the slave instrument.
 2. A The methodaccording to claim 1, wherein the electromagnetic radiation comprisesX-rays.
 3. The method according to claim 1, further comprising:initially measuring at a manufacturing site the plurality of stableobjects on the master instrument, thereby obtaining the set of responsesrepresenting measurements performed with the master instrument (Q_(low)^(m) and Q_(high) ^(m)); initially storing at the manufacturing site theset of responses (Q_(low) ^(m) and Q_(high) ^(m)) initially measured asa set of constant values in the memory, the memory being accessible fromthe slave instrument, when measuring the corresponding stable objects ona slave instrument.
 4. A The method according to claim 1, wherein thedetermination of the correcting function is being based on a regressionmethod.
 5. The method according to claim 4, wherein the regressionmethod is selected from the group consisting of principal componentregression, multiple linear regression, partial least squaresregression, and artificial neural networks.
 6. The method according toclaim 1, wherein the correcting function comprises a plurality of termsof the following form: Q_(low) ^(n1)*Q_(high) ^(m1), wherein n1 and m1are selected from the group consisting of real numbers and integers, andn1 is positive.
 7. The method according to claim 6, wherein thecorrecting function comprises at least three of the following terms:Q_(low), Q_(high), Q_(low) ², Q_(high) ² and Q_(low)/Q_(high).
 8. Themethod according to claim 6, wherein the correcting function comprisesat least three of the following terms: Q_(low)*Q_(high); Q_(low)²*Q_(high); Q_(low)*Q_(high) ²; Q_(low) ²/Q_(high); Q_(low)/Q_(high) ²;Q_(low) ²/Q_(high) ²; and Q_(low) ²/Q_(high) ².
 9. The method accordingto claim 1, wherein the correcting function is of the form:$\frac{Q_{low}^{m}}{Q_{high}^{m}} = {{B_{1}Q_{low}^{s}} + {B_{2}Q_{high}^{s}} + {B_{3}Q_{low}^{s2}} + {B_{4}Q_{high}^{s2}} + {B_{5}Q_{low}^{s}Q_{high}^{s}} + {B_{6}Q_{low}^{s2}Q_{high}^{s}} + {B_{7}Q_{low}^{s}Q_{high}^{s2}} + {B_{8}\frac{Q_{low}^{s}}{Q_{high}^{s}}} + {B_{9}\frac{Q_{low}^{s2}}{Q_{high}^{s}}} + {B_{10}\frac{Q_{low}^{s}}{Q_{high}^{s2}}} + {B_{11}\lbrack \frac{Q_{low}^{s}}{Q_{high}^{s}} \rbrack}^{2} + B_{0}}$wherein the Bs are constants.
 10. The method according to claim 1,further comprising: determining, based on the sets of responses, afurther correcting function, being a functional relationship betweenresponses of the slave instrument (Q_(low) ^(s) or Q_(high) ^(s)) andrelated responses (Q_(low) ^(m) or Q_(high) ^(m)) of the masterinstrument, thereby determining a second set of correcting coefficients,α and β.
 11. The method according to claim 10, wherein the furthercorrecting function is a functional relationship between a high energyresponse of the slave instrument (Q_(high) ^(s)) and the related highenergy response (Q_(high) ^(m)) of the master instrument.
 12. The methodaccording to claim 11, wherein the further correcting function isdetermined by use of univariate linear regression.
 13. The methodaccording to claim 12, wherein the further correcting function is of theform Q_(high) ^(m)=α·Q_(high) ^(s)+β.
 14. The method according to claim1, wherein the set of responses for the master instrument and the set ofresponses for the slave instrument each comprise one pair of relatedresponses for each stable object comprised in the plurality of stableobjects.
 15. The method according to claim 1, wherein the relatedresponses are obtained based on measurements on objects being conveyed.16. The method according to claim 1, wherein each of the responses (Q)is an intensity (I).
 17. The method according to claim 1, wherein eachof the responses (Q) is an intensity (I) corrected with respect to darkcurrent of the detectors.
 18. The method according to claim 1, whereineach of the responses is a transmittance (T) being a ratio between anintensity resulting from measuring an object and a reference intensity.19. The method according to claim 1, wherein each of responses is anabsorbance, A, being defined as the negative logarithm to atransmittance, T, (A=−log(T)).
 20. The method according to claim 19,wherein the logarithm is one of a logarithm base 10 and a naturallogarithm.
 21. The method according to claim 1, wherein the responsesfor both the master and the slave instruments are absorbances, A_(low)and A_(high), being determined by calculating$\frac{A_{low} = {{- {\log_{10}\lbrack \frac{{I_{sample}({low})} - {I_{dark}({low})}}{{I_{air}({low})} - {I_{dark}({low})}} \rbrack}}\quad{and}}}{A_{high} = {- {\log_{10}\lbrack \frac{{I_{sample}({high})} - {I_{dark}({high})}}{{I_{air}({high})} - {I_{dark}({high})}} \rbrack}}}$wherein I_(sample) is the intensity of the radiation detected when theobject is irradiated, I_(dark) is the intensity of the radiationdetected when the object is not irradiated, and I_(air) is the intensityof the radiation detected when no object is present, the intensitiesobtained in a measuring region in respective of the master instrumentand the slave instrument by: exposing the object in the measuring regionto low and high X-ray energies and detecting with detectors theintensities I_(sample)(low) and I_(sample)(high), respectively;detecting the intensities I_(dark)(low) and I_(dark)(high) from saiddetectors when no radiation reaches theme; and exposing said detectorsto the low and high X-ray energies when no object is present in themeasuring region and detecting I_(air)(low) and I_(air)(high),respectively.
 22. The method according to claim 1, wherein each of theresponses is a reflectance (R) expressing the reflectance from thesurface of a respective of the objects.
 23. The method according toclaim 22, wherein the reflectance (R) is linearized, using theKubelka-Munk transform (K/S=(1−R)/2R).
 24. A method of correctingresponses representing measurements for an object performed with a slaveinstrument, said method comprising: determining, based on measurementswith the slave instrument, a pair of related responses (Q_(low) ^(s) andQ_(high) ^(S)); determining a ratio [Q_(low)/Q_(high)]^(corr) using acorrecting function, the correcting function being a functionalrelationship between a ratio of related responses of a master instrumentand a sum of a plurality of terms, each term of the plurality of termsbeing a product of a correcting coefficient (B_(i)) and powers ofrelated responses (Q_(low) ^(s) and Q_(high) ^(s)) of the slaveinstrument, wherein each response is raised to a power being a positiveor negative real number, or zero; providing Q_(high) ^(corr), whereQ_(high) ^(corr) is substantially equal to Q_(high) ^(s), or Q_(high)^(corr) is determined using a further correcting function correlatingQ_(high) ^(corr) with Q_(high) ^(s); and calculating Q_(low) ^(corr) asequal to Q_(high) ^(corr)*[Q_(low)/Q_(high) ^(corr), and therebyproviding a set of corrected responses.
 25. The method according toclaim 24, wherein the further correcting function is of the form:Q_(high) ^(corr)=α·Q_(high) ^(s)+β.
 26. The method according to claim24, wherein the correcting function comprises terms of the followingform: Q_(low) ^(n1)*Q_(high) ^(m1), wherein n1 and m1 are one of realnumbers and integers, and wherein n1 is positive.
 27. The methodaccording to claim 24, wherein the correcting function comprises atleast three of the following terms: Q_(low), Q_(high), Q_(low) ²,Q_(high) ² and Q_(low)/Q_(high).
 28. The method according to claim 24,wherein the correcting function comprising at least three of thefollowing terms: Q_(low)*Q_(high); Q_(low) ²*Q_(high); Q_(low)*Q_(high)²; Q_(low) ²/Q_(high); Q_(low)/Q_(high) ²; Q_(low) ²/Q_(high) ²; andQ_(low) ²/Q_(high) ².
 29. The method according to claim 24, wherein thecorrecting function is of the form:$\lbrack \frac{Q_{low}}{Q_{high}} \rbrack^{corr} = {{B_{1}Q_{low}^{s}} + {B_{2}Q_{high}^{s}} + {B_{2}Q_{low}^{s2}} + {B_{4}Q_{high}^{s2}} + {B_{5}Q_{low}^{s}Q_{high}^{s}} + {B_{6}Q_{low}^{s2}Q_{high}^{s}} + {B_{7}Q_{low}^{s}Q_{high}^{s2}} + {B_{8}\frac{Q_{low}^{s}}{Q_{high}^{s}}} + {B_{9}\frac{Q_{low}^{s2}}{Q_{high}^{s}}} + {B_{10}\frac{Q_{low}^{s}}{Q_{high}^{s}}} + {B_{11}\lbrack \frac{Q_{low}^{s}}{Q_{high}^{s}} \rbrack}^{2} + B_{0}}$wherein the Bs are constants.
 30. The method according to claim 24,wherein each of the responses (Q) is an intensity (I).
 31. The methodaccording to claim 24, wherein each of the responses (Q) is an intensity(I) corrected with respect to dark current of the detectors.
 32. Themethod according to claim 24, wherein each of the responses is atransmittance (T) being a ratio between intensity resulting frommeasuring an object and a reference intensity.
 33. The method accordingto claim 24, wherein each of responses is an absorbance, A, defined asthe negative logarithm to a transmittance, T, (A=−log(T)).
 34. Themethod according to claim 33, wherein the logarithm is one of alogarithm base 10, and a natural logarithm.
 35. The method according toclaim 24, wherein the responses are absorbances being determined bycalculating$\frac{A_{low} = {{- {\log_{10}\lbrack \frac{{I_{sample}({low})} - {I_{dark}({low})}}{{I_{air}({low})} - {I_{dark}({low})}} \rbrack}}\quad{and}}}{A_{high} = {{- {\log_{10}\lbrack \frac{{I_{sample}({high})} - {I_{dark}({high})}}{{I_{air}({high})} - {I_{dark}({high})}} \rbrack}} \pm}}$wherein I_(sample) is the intensity of the radiation detected when theobject is irradiated, I_(dark) is the intensity of the radiationdetected when the object is not irradiated, and lair is the intensity ofthe radiation detected when no object is present, the intensitiesobtained in a measuring region of the slave instrument by: exposing anobject in the measuring region to low and high X-ray energies anddetecting with detectors the intensities I_(sample)(low) andI_(sample)(high), respectively; detecting with the detectors theintensities I_(dark)(low)) and I_(dark)(high) from said detectors whenno radiation reaches them; and exposing said detectors to the low andhigh X-ray energies when no object is present in the measuring regionand detecting I_(air)(low) and I_(air)(high), respectively.
 36. Themethod according to claim 24, wherein each of the responses is areflectance (R) expressing the reflectance from the surface of arespective of the objects.
 37. The method according to claim 36, whereinthe reflectance (R) is linearized using the Kubelka-Munk transform(K/S=(1−R)/2R).
 38. A method of determining a physical quantity for anobject by a slave instrument, the method comprising: determining for theobject corrected high and low energy responses (Q_(high) ^(corr) andQ_(low) ^(corr)) using the method according to claim 24; and determiningthe physical quantity by applying a calibrated functional relationshipbetween Q_(high) ^(corr) and Q_(low) ^(corr) and a physical quantity onsaid corrected responses.
 39. The method according to claim 38, whereinthe calibrated functional relationship is a functional relationshipbetween a physical quantity and a sum of a plurality of terms, each termbeing a product of a calibration coefficient (B_(i)) and powers ofrelated responses (Q_(low) ^(s) and Q_(high) ^(s)), wherein eachresponse is raised to a power being a positive or negative real number,or zero.
 40. The method according to claim 39, wherein the calibratedfunctional relationship comprises terms of the form: Q_(low)^(n1)*Q_(high) ^(m1), wherein n1 and m1 are at least one of real numbersand integers, and wherein n1 is positive.
 41. The method according toclaim 40, wherein the calibrated functional relationship comprises termsof the form: Q_(low), Q_(high), Q_(low) ², Q_(high) ² andQ_(low)/Q_(high).
 42. The method according to claim 40, wherein thecalibrated functional relationship comprises terms of the form:Q_(low)*Q_(high)l Q_(low) ²*Q_(high); Q_(low)*Q_(high) ²; Q_(low)²/Q_(high); Q_(low)/Q_(high) ²; Q_(low) ²/Q_(high) ²; and Q_(low)²/Q_(high) ².
 43. The method according to claim 40, wherein thecalibrated functional relationship is of the form:${F(Q)} = {{B_{1}Q_{low}^{s2}} + {B_{2}Q_{high}^{s}} + {B_{3}Q_{low}^{s2}} + {B_{4}Q_{high}^{s2}} + {B_{5}Q_{low}^{s}Q_{high}^{s}} + {B_{6}Q_{low}^{s2}Q_{high}^{s}} + {B_{7}Q_{low}^{s}Q_{high}^{s2}} + {B_{8}\frac{Q_{low}^{s}}{Q_{high}^{s}}} + {B_{9}\frac{Q_{low}^{s2}}{Q_{high}^{s}}} + {B_{10}\frac{Q_{low}^{s}}{Q_{high}^{s2}}} + {B_{11}\lbrack \frac{Q_{low}^{s}}{Q_{high}^{s}} \rbrack} + B_{0}}$wherein the Bs are constants.
 44. The method according to claim 38,wherein the calibration model is obtained by exposing the masterinstrument to a plurality of well-defined objects.
 45. The methodaccording to claim 44, wherein the well-defined objects are defined suchthat physical properties of the objects have been established by achemical process.
 46. The method according to claim 45, wherein thechemical process is an officially recognized reference method for thedetermination of the physical properties.
 47. The method according toclaim 38, wherein each of the responses (Q) is one of: an intensity (I);a transmittance (T) derived as a ratio between intensity resulting frommeasuring an object and a reference intensity; an absorbance defined asthe negative logarithm to a transmittance (A=−log(T)); and a reflectance(R) expressing the reflectance from the surface of an object, thereflectance (R) being linearized using the Kubelka-Munk transform(K/S=(1−R)/2R).
 48. The method according to claim 47, wherein, theresponses are absorbances, the absorbances being determined bycalculating$\frac{A_{low} = {{- {\log_{10}\lbrack \frac{{I_{sample}({low})} - {I_{dark}({low})}}{{I_{air}({low})} - {I_{dark}({low})}} \rbrack}}\quad{and}}}{A_{high} = {{- {\log_{10}\lbrack \frac{{I_{sample}({high})} - {I_{dark}({high})}}{{I_{air}({high})} - {I_{dark}({high})}} \rbrack}} \pm}}$wherein I_(sample) is the intensity of the radiation detected when theobject is irradiated, I_(dark) is the intensity of the radiationdetected when the object is not irradiated, and lair is the intensity ofthe radiation detected when no object is present, the intensitiesobtained in a measuring region of the slave instrument by: exposing anobject in the measuring region to low and high X-ray energies anddetecting with detectors the intensities I_(sample)(low) andI_(sample)(high) respectively; detecting with the detectors theintensities I_(dark)(low) and I_(dark)(high) from said detectors when noradiation reaches them; and exposing said detectors to the low and highX-ray energies when no object is present in the measuring region anddetecting I_(air)(low) and I_(air)(high), respectively.
 49. A method ofusing a slave instrument for determining physical quantities of anobject by use of dual X-ray radiation, the method comprising: scanningsubstantially all or all of the object using X-ray beams having at leasttwo energy levels, the at least two energy levels including a low energylevel and a high energy level, the high energy level being higherrelatively to the low energy level: detecting the X-ray beams havingpassed through the object for a plurality of areas of the object;determining, for each area of the object, the object's response(Q_(low)) at the low energy level and the object's response (Q_(high))at the high energy level; correcting the responses so determined usingthe correcting method according to claim 24; and determining thephysical quantity by applying a calibrated functional relationshipbetween Q_(high) ^(corr) and Q_(low) ^(corr) and a physical quantity onsaid corrected responses.
 50. The method according to claim 49, whereinthe physical quantity is fat content.
 51. The method according to claim49, wherein the object is at least one of food and feed.
 52. A dataprocessing system for providing a correction for a slave instrument,said system using sets of responses based on detecting at least one ofattenuation, reflection and scattering of electromagnetic radiation inor from an object exposed to said electromagnetic radiation in at leasttwo spectral ranges, the set of responses comprising one or more pairsof related responses (Q_(low) ^(s) and Q_(high) ^(s)) representingmeasurements performed with the slave instrument and a set of responsescomprising one or more pairs of related responses (Q_(low) ^(m) andQ_(high) ^(m)) representing measurements performed with a masterinstrument, said responses being obtained for a plurality of stableobjects, wherein each pair of related responses of the master instrumentcorresponds to a respective pair of related responses of the slaveinstrument, wherein each element in the corresponding pair of responsesof the master instrument corresponds to a respective element in eachpair of responses of the slave instrument, said data processing systemcomprising: an accessing unit configured to access a memory, wherein theresponses (Q_(low) ^(m) and Q_(high) ^(m)) of the master instrumentand/or the responses (Q_(low) ^(s) and Q_(high) ^(s)) of the slaveinstrument are stored; a processor configured to determine, based on thesets of responses, a correcting function, the correcting function beinga functional relationship between a ratio of related responses of themaster instrument and a sum of a plurality of terms, each term being aproduct of a correcting coefficient (B_(i)) and powers of relatedresponses (Q_(low) ^(s) and Q_(high) ^(s)) of the slave instrumentwherein each response is raised to a power being a positive or negativereal number, or zero, thereby determining a first set of correctingcoefficients (B₀; B₁; B₂ . . . ) being multiplied by each of the terms;and a storage unit configured to store the first set of correctioncoefficients (B₀; B₁; B₂ . . . ).
 53. The data processing systemaccording to claim 52, wherein the electromagnetic radiation comprisesrays.
 54. The data processing system according to claim 52, furthercomprising: a processor configured to determine a further correctingfunction, the further correcting function being a functionalrelationship between a high energy response of the slave instrument(Q_(high) ^(s)) and related high energy response (Q_(high) ^(m)) of themaster instrument, thereby determining a second set of correctingcoefficients, α and β.
 55. The data processing system according to claim52, wherein each of the responses (Q) is one of: an intensity (I); atransmittance (T) derived from intensity as a ratio between intensityresulting from measuring an object and a reference intensity; anabsorbance, A, being defined as the negative logarithm to atransmittance, T, (A=−log(T)); and a reflectance (R) expressing thereflectance from the surface of an object, the reflectance (R) beinglinearized using the Kubelka-Munk transform (K/S=(1−R)/2R).
 56. A dataprocessing system according to claim 55, wherein the responses areabsorbances, the absorbances being determined by calculating$\frac{A_{low} = {{- {\log_{10}\lbrack \frac{{I_{sample}({low})} - {I_{dark}({low})}}{{I_{air}({low})} - {I_{dark}({low})}} \rbrack}}\quad{and}}}{A_{high} = {- {\log_{10}\lbrack \frac{{I_{sample}({high})} - {I_{dark}({high})}}{{I_{air}({high})} - {I_{dark}({high})}} \rbrack}}}$wherein I_(sample) is the intensity of the radiation detected when theobject is irradiated, I_(dark) is the intensity of the radiationdetected when the object is not irradiated, and lair is the intensity ofthe radiation detected when no object is present, the intensitiesobtained in a measuring region of the slave instrument by: exposing anobject in the measuring region to low and high X-ray energies anddetecting with detectors the intensities I_(sample)(low) andI_(sample)(high), respectively; detecting with the detectors theintensities I_(dark)(low) and I_(dark)(high) from said detectors when noradiation reaches them; and exposing said detectors to the low and highX-ray energies when no object is present in the measuring region anddetecting I_(air)(low) and I_(air)(high), respectively.
 57. A correctingsystem comprising a slave instrument for obtaining responses and a dataprocessing system for correcting the responses, the responsesrepresenting measurements performed with the slave instrument and theresponses based on detecting by the slave instrument at least one ofattenuation, reflection and scattering of electromagnetic radiation inor from an object exposed to said electromagnetic radiation in at leasttwo spectral ranges, the set of responses comprises one or more pairs ofrelated responses (Q_(low) ^(s) and Q_(high) ^(s)), said correctingsystem comprising: a first processor means for determining the one ormore pairs of related responses (Q_(low) ^(s) and Q_(high) ^(s)) basedon measurements on an object with the slave instrument; a secondprocessor means for performing a correction of responses using acorrection according to claim 24, said second processor means comprisingan accessing unit configured to access a memory storing a first set ofcorrection coefficients (B₀; B₁; B₂ . . . ); a third processor means fordetermining the ratio [Q_(low)/Q_(high)]^(corr) by the correctingfunction; a fourth processor means for determining the corrected highenergy response Q_(high) ^(corr) by the further correcting function; anda fifth processor means for determining the corrected low energyresponse Q_(low) ^(corr) by multiplying [Q_(low)/Q_(high)]^(corr) byQ_(high) ^(corr).
 58. The system according to claim 57, wherein theelectromagnetic radiation comprises x-rays.
 59. The system according toclaim 57, wherein each of the responses (Q) is one of: an intensity (I);a transmittance (T) derived from intensity as a ratio between intensityresulting from measuring an object and a reference intensity; anabsorbance, A, being defined as the negative logarithm to atransmittance, T, (A=−log(T)); and a reflectance (R) expressing thereflectance from the surface of an object, the reflectance (R) beinglinearized using the Kubelka-Munk transform (K/S=(1-R)/2R).
 60. Thesystem according to claim 52, further comprising: a storage unitconfigured to store at least one of: a set of responses (Q_(low) ^(m)and Q_(high) ^(m)) for the set of stable objects measured on the masterinstrument, the first set of correction coefficients (B₀; B₁, B₂ . . .), and the further correcting function.
 61. A set comprising one or morestable objects for, or used during, carrying out a method according toclaim 1, each object comprising at least two different chemicalcompositions which are substantially stable, and each stable objecthaving a response property.
 62. The set of stable objects according toclaim 61, wherein the response property is absorbance.
 63. The set ofstable objects according to claim 61, wherein for each of the stableobjects a first member of the at least two different chemicalcompositions is one having X-ray response properties similar to adiposetissue, and a second member of the at least two different chemicalcompositions is one having X-ray response properties similar to muscletissue.
 64. The set of stable objects according to claim 63, wherein theresponse properties of the first and second members are absorbance. 65.The set of stable objects according to claim 61, which the stableobjects have varying thickness and/or areal density.
 66. The set ofstable objects according to claim 65, wherein the stable objects areintegrated into a single stepped item.
 67. The set of stable objectsaccording to claim 61, wherein each object comprised in the set ofobjects is stable such that the X-ray response properties of the objectdo not change more than 0.1% over a prescribed period of at least 10days.
 68. The set of stable objects according to claim 66, wherein theprescribed period is at least 1 month.
 69. The set of stable objectsaccording to claim 66, wherein the prescribed period is at least 1 year.70. The set of stable objects according to claim 66, wherein the X-rayresponse properties of the object do not change more than more than0.01% over the prescribed period.
 71. The set of stable objectsaccording to claim 66, wherein the X-ray response properties of theobject do not change more than more than 0.001% over the prescribedperiod.
 72. The set of stable objects according to claim 61, wherein thenumber of stable objects in the set of stable objects is at least
 8. 73.The set of stable objects according to claim 72, wherein the number ofstable objects in the set of stable objects is at least
 12. 74. The setof stable objects according to claim 72, wherein the number of stableobjects in the set of stable objects is at least
 15. 75. The set ofstable objects according to claim 72, wherein the number of stableobjects in the set of stable objects is at least
 20. 76. The set ofstable objects according to claim 72, wherein the number of stableobjects in the set of stable objects is at least 26.